Related papers: Discrete phase-space structure of $n$-qubit mutual…
If a pure state of a qubit pair is developed over the four basis states, it is known that an equality between the four coefficients of that development exists if and only if that state is unentangled. This paper considers an arbitrary pure…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
One way to construct a maximal set of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of…
We investigate dynamical quantum phase transitions in disordered quantum many-body models that can support many-body localized phases. Employing $l$-bits formalism, we lay out the conditions for which singularities indicative of the…
We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into…
An ideal system of $n$ qubits has $2^n$ dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can…
In a quantum system having a finite number $N$ of orthogonal states, two orthonormal bases $\{a_i\}$ and $\{b_j\}$ are called mutually unbiased if all inner products $<a_i|b_j>$ have the same modulus $1/\sqrt{N}$. This concept appears in…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
We investigate the classical phase space structure of $N$ $SU(n+1)$ non-Abelian Chern-Simons (NACS) particles by first constructing the product space of associated $SU(n+1)$ bundle with ${\bf CP}^n$ as the fiber. We calculate the Poisson…
We extract the phase coherence of a qubit defined by singlet and triplet electronic states in a gated GaAs triple quantum dot, measuring on timescales much shorter than the decorrelation time of the environmental noise. In this non-ergodic…
We show that with the assistance of a third level of the qubits an n-qubit phase gate can be constructed from $2n-4$ two-qutrit conditional swap gates, a single qutrit-qubit controlled phase gate, and two single-qutrit operations. Unlike…
The connection between maximal sets of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space and finite phase-space geometries is well known. In this article we classify MUBs according to their degree of covariance with…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase…
We define a notion of facets-pairing structure and its seal space on a nice manifold with corners. We will study facets-pairing structures on any cube in detail and investigate when the seal space of a facets-pairing structure on a cube is…
The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully…
We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are…
A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p^k, where p is a prime number. They mesh naturally with finite affine planes of order N, that exist when N = p^k. The existence of MUBs for…
We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamio{\l}kowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the…